Why physicists think geometry is the path to a theory of everything

Can you imagine the imprint that a hexagon four dimensions could leave by crossing your three-dimensional kitchen table? Probably not, but some people can.

One of these people was the mathematician Alicia Boole Stott, daughter of the logician George Boole. At the beginning of the 20th century, she made models of four -dimensional objects of forms creating during the passage of three -dimensional objects. Decades later, when mathematicians could verify such things using computer programs, they found that Boole Stott had had a strange gift to obtain these correct forms.

For most of us, geometry evokes thoughts of pencils, leaders, triangles and circles. This means these complicated questions that you asked at school involving parallel lines and angles. But as the history of Boole Stott shows, the researchers have been taking geometry far beyond a while.

Geometry can move away from the understandable world of two -dimensional and three -dimensional forms – and, in doing so, it can be extremely enlightening. The best example is perhaps general relativity, the theory of gravity of Albert Einstein, who joins the three dimensions of space over time, creating a four-dimensional stage on which everything in the universe is played out.

But geometry can also use dimensions that are not physically real. Think of meteorology, for example, where a point in the atmosphere can have many “dimensions” – latitude, longitude, temperature, pressure, wind speed, etc.

Researchers map these dimensions as forms that extend to higher dimensions to help understand the functioning of the atmosphere. “According to things like this, you can apply mathematical models and determine what happens to [those properties] In many dimensions, ”explains the mathematician Snezana Lawrence at Middlesex University in London.

For theoretical physicists, the additional dimensions seem to be a necessary part of any complete description of the universe, some proposing that our reality is a “projection” of a higher dimension, for example. It may seem bizarre, but if physicists make certain simplification hypotheses linked to this idea, it suddenly makes it possible to do calculations to do with fundamental particles and black holes which are otherwise impossible.

Some physicists are betting on even stranger geometric ideas being a path to a “theory of everything”, a single frame that explains the cosmos and everything it contains. One of them is “amplituhedron”, a mathematical object developed by Jaroslav Trnka at the University of California, Davis and Nima Arkani at the Institute of Advanced Study, New Jersey. Consider this as an abstract multidimensional crystal, whose properties provide another way of describing the fundamental principles of particle physics.

Or there is a “dynamic causal triangulation”, developed by Renate Loll at Radboud University in the Netherlands. This covers a set of geometric forms together to create a description of space -time which seems to have some of the properties of quantum theory and general relativity – two ideas which are normally incompatible. It is, she says, not only an abstract geometric notion, but a reflection testable of the real properties of the universe which could be reflected in our observations of the microwave cosmic background which fills the entire space.

None of these ideas still represents a theory of everything. But some suspect that to have a hope of finding one, we need a new vision of physics – and there is a growing feeling that it could be written in the language of geometry. Whether true or not, geometry is certainly more than hexagons – even in four dimensions.